Data-driven multi-attribute decision-making by combining probability distributions based on compatibility and entropy
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Data-driven multi-attribute decision-making by combining probability distributions based on compatibility and entropy Hengqi Zhang1 · Wen Jiang1
· Xinyang Deng1
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Multi-attribute decision-making has many applications in different fields. How to make decisions objectively when there are many attributes is still an open issue. This paper proposes a data-driven multi-attribute decision-making method considering the compatibility and entropy. Mainly, data of different decision attributes are normalized to probability distributions. The compatibility weight and entropy weight are computed respectively and then combined to a final weight. The scores of decision objects are derived by combining weighted probability distributions. In order to verify the effectiveness of the proposed method, two examples are given to compare with the AHP method and an improved data envelopment analysis method respectively. The former results show that the proposed method can obtain more objective results and produce a low computation complexity. The latter demonstrate the proposed method focuses more on the overall performance of decision attributes while the improved data envelopment analysis emphasises more on the ecological performance. Keywords Multi-attribute decision-making · Normalization · Probability distribution · Compatibility weight · Entropy weight
1 Introduction Multi-attribute decision-making (MADM) is a hot research field and has a wide application in many other fields [4, 15, 38, 46, 52], such as risk assessment [19, 48]. Rational decision making can help to improve efficiency and avoid risks, which has important research value. Among many multi-attribute decision-making studies, the Analytical Hierarchy Process (AHP) proposed by Saaty is a typical method to deal with multi-attribute decision issues [37]. Comparison matrix of AHP provides a criterion to rank the importance of different attributes. The Technique for Preference by Similarity to an Ideal Solution (TOPSIS), first developed by Hwang et al. [30] and further developed by others, Wen Jiang
[email protected] Hengqi Zhang [email protected] Xinyang Deng [email protected] 1
School of Electronics and Information, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, China
including [25] and [31], is also a typical multi-criteria decision analysis method. Many researches based on AHP and TOPSIS have been conducted. For example, Yong Deng improved AHP with fuzzy number and proposed the fuzzy AHP [9]. An extended TOPSIS method under intervalvalued intuitionistic fuzzy environment was proposed by Gupta et al. [17]. TOPSIS combined with fuzzy number was adopted to failure mode and effects analysis [2]. In recent years, the development of information fusion theory offers a possible way for decision making. Decision making based on D-S evidence theory and fuzzy theory are two important branches and research hotspots. DempsterShafer (D-S) evidence theory is a reaso
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